The present invention relates to a mathematical model and a method and apparatus for utilizing the model. More particularly, the present invention relates to a model, such as a model of the human heart and thorax, that can be used as a tool to improve the manner in which medical imaging techniques are performed in order to enable the occurrence of artifacts in reconstructed images acquired through these techniques to be reduced or eliminated. The present invention also relates to the method and apparatus for utilizing the model in an imaging system simulation.
When using x-ray CT to acquire x-ray projection data to be used in reconstructing an image of human anatomy, it is necessary that the patient not move during the scanning interval. If the patient moves, the x-ray projection data set will be inconsistent in mathematical terms, which will result in image artifacts appearing in the reconstructed images. Generally, the back-projection process used in CT reconstruction smears filtered projection data across a reconstruction grid at each view angle where data is acquired. If the data set is mathematically consistent, i.e., acquired from a stationary object, constructive interference of the back-projected data will result in features appearing in the reconstructed image, while destructive interference will result in features being eliminated in the reconstructed image. If the patient moves during the scanning process, the interference patterns will be altered, thereby resulting in image artifacts appearing in the reconstructed image.
In some instances, it is difficult or impossible for the patient to remain stationary. Respiratory motion can be minimized by having the patient hold his or her breath. However, cardiac motion cannot be reduced. As a result, image artifacts occur in reconstructions of the heart and surrounding tissue. One method that is used to reduce such artifacts is to decrease the scanning time. However, decreasing the scanning time may result in significantly increasing system complexity and cost. A better, and yet unexplored, solution would be to optimize existing hardware and algorithms to improve the temporal resolution of reconstructed images. Once an understanding of the system design tradeoffs are evaluated, it would be possible to make system improvements without having to design new complex and costly systems.
Since patients"" heart rates and electrocardiograms (ECG) vary significantly from patient to patient, it would be useful to devise a mathematical four-dimensional (4-D) (i.e., 3-D spatial and 1D temporal) model of the heart and surrounding tissue in the chest that could be used in research to determine the manner in which the heart should be imaged in order to improve the quality of the reconstructed images. Using such a model in a simulation of an imaging system, such as a CT system, would allow the motion of the heart to be controlled in a systematic way, thereby enabling the performance of the imaging system to be quantified. The model could also be used in the simulations to identify the nature of the image artifacts, which would facilitate the development of various data preprocessing algorithms that would reduce or eliminate such artifacts.
One approach that has been used to generate a 4-D model of the heart is to acquire patient data, generate a 3-D reconstruction of the chest enclosing the heart at various times during the cardiac cycle, segment the reconstructions, and generate surfaces that comprise the anatomy of the heart. The reconstructions at various instants in time are then combined to generate a 4-D model of the heart. Using these techniques, the ventricular and atrial chambers, as well as major vessels (Vena Cava Caudal, Vena Cava Cranial, Aorta, pulmonary veins, pulmonary arteries) connected to the heart, could be segmented.
One disadvantage of this technique is that since the data is acquired from an actual patient over a specified time interval, it is difficult, if not impossible, to determine fine structures in the anatomy of the heart due to cardiac motion. For instance, coronary vessels are difficult to segment and/or are difficult to determine from the reconstructed volumes. One primary application in cardiac imaging is the assessment of stenosis in coronary arteries. If the extent of the stenosis could be reliably identified and quantified, the clinical impact on patient diagnosis and/or treatment could be significant. The aforementioned modeling technique is limited in this regard.
Accordingly, a need exists for a model of the heart that overcomes the deficiencies associated with the aforementioned model. More particularly, a need exists for a model of the heart that is based on mathematical basis objects, rather than on actual data acquired from a patient. The basis objects mathematically define the structure of the model to thereby enable an accurate 4-D representation of the heart to be generated. The model can be used in imaging system simulations to optimize data acquisition protocols and data processing algorithms so that the motion of the heart can be xe2x80x9cfrozenxe2x80x9d to prevent imaging artifacts from occurring in the reconstructed image.
The present invention provides a mathematical model and apparatus for utilizing the model to simulate an imaging scenario. The model is comprised of basis objects, each basis object being defined by a mathematical function. Each basis object has a spatial relationship to the other basis objects, the basis objects and the spatial relationship defining a three-dimensional geometry of the model. The model is stored on a computer-readable medium and is capable of being transformed by one or more transformation operations, each transformation operator corresponding to a predetermined transformation operation, wherein when one of the transformation operators operates on one of the basis objects, the spatial relationship between the basis object that is operated on at least one other basis object is varied, thereby causing the geometry of the model to be varied.
These and other features and advantages of the present invention will become apparent from the following description, drawings and claims.